On the Kac-rice Formula

نویسنده

  • LIVIU I. NICOLAESCU
چکیده

This is an informal introduction to the Kac-Rice formula and some of its (mostly one-dimensional) applications.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Inference in Adaptive Regression via the Kac-Rice Formula

We derive an exact p-value for testing a global null hypothesis in a general adaptive regression setting. Our approach uses the Kac-Rice formula (as described in Adler & Taylor 2007) applied to the problem of maximizing a Gaussian process. The resulting test statistic has a known distribution in finite samples, assuming Gaussian errors. We examine this test statistic in the case of the lasso, g...

متن کامل

On the Zeros of Random Harmonic Polynomials: the Truncated Model

Inspired by Wilmshurst’s conjecture, W. Li and A. Wei (2009) initiated a probabilistic study concerning the zeros of harmonic polynomials. They derived a Kac-Rice type formula for the expected number of zeros of random harmonic polynomials p(z) + q(z) with independent Gaussian coefficients. They also provided asymptotics in the case when p and q are sampled independently from the the (complex) ...

متن کامل

Application of semi-analytic method to compute the moments for solution of logistic model

The population growth, is increase in the number of individuals in population and it depends on some random environment effects. There are several different mathematical models for population growth. These models are suitable tool to predict future population growth. One of these models is logistic model. In this paper, by using Feynman-Kac formula, the Adomian decomposition method is applied to ...

متن کامل

On the Optimization Landscape of Tensor Decompositions

Non-convex optimization with local search heuristics has been widely used in machine learning, achieving many state-of-art results. It becomes increasingly important to understand why they can work for these NP-hard problems on typical data. The landscape of many objective functions in learning has been conjectured to have the geometric property that “all local optima are (approximately) global...

متن کامل

Sporadic groups and string theory

whereW is the Weyl group, ρ is the Weyl vector, and the product is over all positive roots α. This is a special case of Weyl’s character formula which says that the character of a finite dimensional representation is equal to a sum similar to the left hand side divided by the product on the right hand side; for the 1-dimensional representation the character is 1 so the sum is equal to the produ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2014